Analytical study of superconducting RF cavity detuning compensation

TL;DR

This paper provides an analytical framework for understanding how PI feedback loops stabilize superconducting RF cavities against microphonic detuning, simplifying the analysis under typical operating conditions.

Contribution

It introduces a linearized model of cavity detuning response, enabling straightforward analysis of PI loop performance based on system parameters.

Findings

Linearized response model for small detuning amplitudes

Analytical expressions for PI loop stability and performance

Insights into parameter effects on cavity stabilization

Abstract

The cavities in superconducting linacs tend to operate with narrow bandwidths that are comparable to microphonic induced detuning from external forces. Proportional-Integral (PI) feedback loops are used to stabilize the cavity voltage in response to the varying cavity resonant frequency. Without feedback, the cavity voltage variation with detuning is non-linear, but in this paper we show that in the regime where the detuning amplitude is smaller than the frequency of the detuning, which is typically the case, the response can be linearized so as to provide simple analytical characterizations of PI loop performance as a function of the various parameters involved (integral and proportional gains, noise and low pass filter bandwidth).